Worry about Republican that is becoming most incensed (8)
I believe the answer is:
angriest
'most incensed' is the definition.
('angry' can be similar in meaning to 'incensed')
'worry about republican that is' is the wordplay.
'worry' becomes 'angst' (I've seen this in another clue).
'about' indicates putting letters inside.
'republican' becomes 'R' (abbreviation).
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'r'+'ie'='rie'
'angst' enclosing 'rie' is 'ANGRIEST'.
'becoming' acts as a link.
(Other definitions for angriest that I've seen before include "Most wrathful" , "Most characteristic of 1950s young men" , "Most incensed kind of ingrates" , "Most irate and furious" , "Extremely mad" .)