Military cap given by king, most majestic (4)
I believe the answer is:
kepi
'military cap' is the definition.
(I've seen this before)
'by king most majestic' is the wordplay.
'by' says to put letters next to each other.
'king' becomes 'K' (abbreviation for king in chess).
'most' means to remove the last letter.
'majestic' becomes 'epic' (both can mean grand).
'epic' with its final letter taken away is 'epi'.
'k'+'epi' is 'KEPI'.
'given' is the link.
(Other definitions for kepi that I've seen before include "French army cap" , "Service cap" , "Flat-topped military cap" , "French military cap" , "French military hat" .)