Twinge of deep anger (4)
I believe the answer is:
pang
'twinge' is the definition.
(I know that twinge can be written as pang)
'of deep anger' is the wordplay.
'of' indicates the answer is hidden within the clue.
'PANG' can be found hidden inside 'deep anger'.
(Other definitions for pang that I've seen before include "Sharp emotional pain" , "Sudden feeling of pain or conscience" , "Sudden sharp pain" , "Stab of emotion" , "Short violent pain" .)