Way chief shows formality (6)
I believe the answer is:
starch
'formality' is the definition.
(being excessively formal or stiff)
'way chief' is the wordplay.
'way' becomes 'st' (abbreviation for street).
'chief' becomes 'arch' (synonyms).
'st'+'arch'='STARCH'
'shows' is the link.
(Other definitions for starch that I've seen before include "Carbohydrate; stiffen" , "Reserve" , "Potato, rice constituent; a stiffener" , "foodstuff" , "Stiffening carbohydrate" .)