I'm a procrastinator, myself. So I have to chuckle heartily at
How can I make my partner realise it's better to do things on time?
Have you considered the possibility that it isn't better? If you haven't considered the possibility that procrastinating is better, how can you reasonably expect your partner to consider the possibility that doing things on time is better?
Sounds almost backwards, right? It actually turns out that there's a lot of situations where procrastination is indeed better. For example, some things turn out not to need to get done. Other things reveal an easier way of doing them, given enough time. Other times the procrastinator is looking at the big picture, rather than the artificial walls we erect to make sense of life. There's actually a lot of good rational arguments for procrastination.
There's also lots of pretty poor arguments for procrastination. I know. I've made them myself. Lazyness feels good!
As other posters have mentioned, you cant fix procrastination by pushing. It takes some pulling. My recommendation is to start a dialog with your partner to try to learn why they procrastinate. I just listed three good reasons to procrastinate. Perhaps he has a good reason? I didn't list any bad reasons to procrastinate. That's pure self-preservation. If my wife reads this, she must not know all of my bad reasons =)
When having this dialogue, not only should you be ready for your partner to question why you want to get things done "on time," you should encourage it. There are good reasons to get everything done "on time." There's also some pretty poor ones also. If you're making your partner explore their motivation, you should be ready to explore your own motivation as well.
I expect your partner has some good reasons for procrastination, but if they're like me, they also have a lot of bad reasons. This is where you can strike. Make it easier to make it easier to stop procrastinating. You don't have to stop them from procrastinating. You have to get them on the path such that they act to stop procrastinating on their own accord.
It's not an easy path. Neither is living together. It's also not a short path, so you will have to find solutions in the interm. For example:
But it is very important to me to have free time and be relaxed rather than be anxious about chores that have to be done, but haven't yet. Sometimes I have no proper clothes to wear because they haven't been ironed when they should have been.
The first sentence is a personal thing. It's your style. It's not right; it's not wrong. Its you. How does your partner feel about that? Do they empathize with the stress this is causing you? Do they even know you're stressing out?
The second sentence is concrete. This is actionable. This is a point where that procrastination has generated consequences which you cannot simply work around (presuming having proper clothes to wear really is a necessity). Do they understand how much frustration this caused? Do they have a plan for how to make sure it doesn't happen in the future? Do you have a plan for if they fail?
Depending on how deep the procrastination goes, you may have to take on the essential tasks which have deadlines that cannot be missed. You might have to make sure at least X outfits are ready-to-go at any time, even if you have to iron them yourself. Is that right? Is that fair? No idea. We all get to write the book on our own relationship. In every relationship we have to figure these things out for ourselves. For example:
Chores are equally divided. We work the same hours and arrive at home at the same time
Is "equally divided" actually the best division? Your mind seems to be better geared towards tasks that are organized as "chores." Equally divided chores might actually be thought of as more work for him! Of course, unequal division opens the door for all sorts of laziness, so we have to be careful.
Consider using the concept of Pareto Optimality. A system is Pareto Optimal if there's no reallocation of resources (or tasks) which could make one person better off without making anyone else worse off. The classic example is the school lunch trading game. If I have an apple and want a cookie, and you have a cookie and want an apple, we can trade and make the situation more optimal. However, if you have an apple and want a cookie, and I have 100 cookies and no interest in apples, there is no Pareto optimal trade to be made. Anything which gives you a cookie makes me worse off.
Right now your chores are equally divided. Chores are easy to divide equally. But widen it to the larger scope of the relationship. What trades could be made that benefit both of you?
Since I don't know you or your partner as people, I'll have to make up a contrived example. Maybe you like to really kick butt during the day, but doing that leaves you vulnerable and open to people taking cheap shots at you that makes you feel crummy. Maybe he might want to comfort you, but his mind is busy trying to procrastinate on all those chores. There may be a trade where you take on some of his chores, and he understands that part of that agreement is that he better be there for you when you need someone after a bad day -- it's part of the trade.
The Pareto Optimality can change over time. It will change over time. You're constantly finding the best balance for your relationship.
My wife and I are still striking that balance. She's a go-getter, like you describe yourself, who always wants everything done. I'm a procrastinator who works longer hours than she does, coming home mentally numbed from work. Right now she takes on the vast majority of the chores. But if she's had a tough day (or a tough week), it's expected that I'll pitch in on the chores, even the chores that "aren't mine," even if I had a hard day myself. That balance is working well for us now. We're constantly adjusting it (mostly finding ways to convince my procrastinator side to take on more chores). Ask the same question in a month, and you will get a different answer. That's life!