Solemn head of organisation holding right hat (8)
I believe the answer is:
sombrero
'hat' is the definition.
(I know that sombrero is a type of hat)
'solemn head of organisation holding right' is the wordplay.
'solemn' becomes 'somber' (synonyms).
'head of' suggests taking the first letters.
'holding' is an insertion indicator.
'right' becomes 'r' (abbreviation).
The initial letter of 'organisation' is 'o'.
'somber'+'o'='sombero'
'sombero' going around 'r' is 'SOMBRERO'.
(Other definitions for sombrero that I've seen before include "a Mexican's overheads" , "Large hat from Mexico" , "Straw hat with very wide brim from Mexico" , "Hat for South American" , "Large Mexican sun-hat" .)