Put in dash of neat rum husband found in promotion at first (9)
I believe the answer is:
hyphenate
'put in dash' is the definition.
(put in hyphen)
'neat rum husband found in promotion at first' is the wordplay.
'rum' is an anagram indicator (rum can mean strange or unusual).
'husband' becomes 'h'.
'found in' is an insertion indicator.
'promotion' becomes 'hype' (hype is a kind of promotion).
'at first' means one lot of letters go next to another.
'h' put within 'hype' is 'hyphe'.
'neat' with letters rearranged gives 'nate'.
'nate' put after 'hyphe' is 'HYPHENATE'.
'of' is the link.
(Other definitions for hyphenate that I've seen before include "How to combine handles, for example" , "Add dash" , "Join two words with horizontal dash" , "Join two words or syllables with short dash" , "with short line" .)