Clue: Minstrel with instrument entertaining king, old and gloomy (10)
Answer: TROUBADOUR
Explanation: Definition: Minstrel
A charade of TROUBA, an envelope ('entrtaining') of R (*Rex*, 'king') plus O ('old') in TUBA ('instrument'); plus DOUR ('gloomy'). Having the ending D-U-, I had difficulty getting DRUM out of my head.