Why were there Tony Stark's clothes on-board the Quinjet which ended up on Sakaar?

It stands to reason that the Quinjet that the Avengers used would have been equipped for the Avengers. In this case each having a compartment to store some stuff they might need, in Tony’s case this also means storing some extra clothes.

However, it’s worth noting that the Quinjet was last seen on Earth when the Avengers were saving Sokavia from Ultron. It makes sense it was equipped with equipment for the team even if it wasn’t normally as they had just been using it. Tony being egotistical likely had a spare suit in case his current got damaged so he could still look the part after the battle.

Out of universe though Taiki put it in for a joke because of how Tony’s clothes have always looked. Costume designer Mayes Rubeo has the following to say:

I think it was Taika or [producer] Brad Winderbaum, our creative executive. It just goes into the bible of the '80s, and what would Tony Stark wear? We make his pants tight, and everything is a little tight because it's more fitted for Tony Stark, of course. And we made a joke about it. So you know, it worked.

_{Cinema Blend, How Thor: Ragnarok's Tony Stark Joke Came Together}

Taiki says the following on the director's commentary track for Thor: Ragnarok according to this reddit post but I have yet to fact check it.

Taiki Waititi: I really wanted to make fun of Tony Stark’s clothes because I think in some of those movies, they seem very funny to me. Some of the funny T-shirt designs and his funky trendy clothes that he always wears.