Collocations for moustache - noun

thick, thin
long
small
bushy, curly, droopy, handlebar, neat (esp. BrE), pencil (BrE), toothbrush (BrE), walrus (esp. BrE), waxed (esp. BrE)
fake (esp. AmE), false (esp. BrE)

have, sport, wear
Her fiancé sported a bushy moustache.

grow
He's trying to grow a moustache.

trim
shave off
stroke, twirl
He stroked his moustache thoughtfully.