Starts to sketch the elderly Texan relative's hat (7)
I believe the answer is:
stetson
'hat' is the definition.
(Stetson is an example)
'starts to sketch the elderly texan relative's' is the wordplay.
'starts to' says to take the initial letters.
'relative' becomes 'son' (son is a kind of relative).
The first letters of 'sketch the elderly texan' is 'stet'.
'stet'+'son'='STETSON'
(Other definitions for stetson that I've seen before include "Style of hat" , "Hat for country-and-western singers, Texan oil magnates, etc." , "A wide-brimmed cowboy hat" , "Large hat" , "Man's hat with wide brim and high crown" .)