The whole clue — Drinking hole where one may buy round after round — is doing double duty as both definition and wordplay in one smooth surface. It's a cryptic all-in-one, pointing to the clubhouse bar at a golf course, which golfers call the nineteenth hole: it's the bar you reach after an eighteen-hole round, where you might then buy a round of drinks. The genius of it is that "round" works on both levels simultaneously — golf rounds and drinks rounds — with no separate letter-by-letter construction needed.