A colloquial expression meaning to have a (usually quick) drink; to grab a drink.
仕事帰りに同僚と居酒屋で一杯引っ掛けた。
On the way home from work I grabbed a drink with colleagues at an izakaya.
時間があれば今夜軽く一杯ひっかけよう。
If there's time, let's have a quick drink tonight.
彼は試験が終わると友達と一杯引っ掛けて祝う習慣がある。
He has a habit of celebrating exams by having a drink with friends.