Cool customer, initially wearing tartan (6)
I believe the answer is:
placid
'cool' is the definition.
(thesaurus)
'customer initially wearing tartan' is the wordplay.
'initially' suggests taking the first letters.
'wearing' is an insertion indicator.
'tartan' becomes 'plaid' ('plaid' can be a synonym of 'tartan').
The initial letter of 'customer' is 'c'.
'c' going within 'plaid' is 'PLACID'.
(Other definitions for placid that I've seen before include "Imperturbable" , "Tranquil, even-tempered" , "Still - US lake" , "Calm, unruffled" , "Calm, peaceful" .)