If your gig is new You didn't get any order on your gig ( that means your gig is new ) then you can deleted your gig it won't be create any problem for your Fiverr Account.
But If your gig is ( selling gig ) that mean's you completed order any gig and get review then you shouldn't be deleted that kind of gig.
Then it will be affected your account!
like you lose can be lost your Rank!!
Thank you.