Should I wait until after I sign a new lease to request another credit card?

Hi!

I’m in my mid-twenties, financially secure but a little late in the game in terms of building my credit. I have one credit card for which I was approved last August (a very basic Capital One Platinum card which has since been upgraded by Capital One), and, now that I’ve got ~four months of on-time payments, I’d like to apply for another credit card to increase available credit and decrease credit utilization.

But I’m also looking for a new apartment, which I’m hoping to move into within the next month. I understand that seeking credit can reflect poorly on my credit score, so should I wait to get another credit card until after I finish applying for apartments?

Thanks!

Edit: I have a 718 right now, if that matters.