Well-regarded Unionist welcomed by theatre board (9)
I believe the answer is:
reputable
'well-regarded' is the definition.
(I've seen this before)
'unionist welcomed by theatre board' is the wordplay.
'unionist' becomes 'u' (abbreviation as in Democratic Unionist Party).
'welcomed by' indicates putting letters inside (letters welcomed inside).
'theatre' becomes 'rep' (repertory theatre).
'board' becomes 'table' (both can mean food).
'rep'+'table'='reptable'
'u' inserted into 'reptable' is 'REPUTABLE'.
(Other definitions for reputable that I've seen before include "Well thought of" , "Trustworthy" , "Honest" , "Respected" , "Upright" .)