expression, godan verb (-tsu)
sing someone's praises; give someone a boost
Idiomatic expression meaning to flatter or support someone, often to gain favor. The literal meaning is 'to carry a lantern' (for someone), which is the origin of the phrase.
See also: 提灯持ち (ちょうちんもち)
彼は上司の提灯を持ってばかりいる。
He's always singing his boss's praises.
あの人は誰にでも提灯を持つから信用できない。
That person flatters everyone, so I can't trust them.