The term complement describes that post-head (verb) sentence element that completes the meaning of the phrase.

Pre-head string Head Post-head string
Peter plays the piano
Peter plays the piano beautifully.
Peter likes coffee with milk
complement adjunct

Generally, complements differ from adjuncts in that complements are obligatory, adjuncts are optional. Adjuncts are stackable, i.e. you can stack more multiple adjuncts onto one another:

Peter plays the piano beautifully in the living room.

On the difference between complements and adjuncts, see: