Hesitated to make a friendly gesture to a leftist (7)
I believe the answer is:
wavered
'hesitated' is the definition.
('waver' can be a synonym of 'hesitate')
'a friendly gesture to a leftist' is the wordplay.
'a friendly gesture' becomes 'wave' (wave is a kind of gesture. I am not sure about the 'friendly' bit.).
'to a leftist' becomes 'red' (red is a kind of leftist).
'wave'+'red'='WAVERED'
'to make' acts as a link.
Can you help me to learn more?
(Other definitions for wavered that I've seen before include "'Vacillated, hesitated (7)'" , "Fluctuated" .)