To Decline, To Restrain, To Refrain
する verb
If 遠慮 is "decline" or "restrain" then the verb vocab version is to decline or to restrain.
えんりょする
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own. Also, the reading comes from 遠慮.
明日、健康診断なので、できれば今日はお酒はご遠慮させてください。
Tomorrow is my physical check-up, so I’d rather not have alcohol today, if that’s okay.