Beat peculiar brother without hesitation (5)
I believe the answer is:
throb
'beat' is the definition.
(throbbing is a kind of beating)
'peculiar brother without hesitation' is the wordplay.
'peculiar' indicates anagramming the letters (I've seen this in other clues).
'without' indicates named letters should be taken away.
'hesitation' becomes 'er'.
'brother' with 'er' removed is 'broth'.
'broth' with letters rearranged gives 'THROB'.
(Other definitions for throb that I've seen before include "Palpitate, quiver (with emotion)" , "Sound of engines" , "Strong regular beat" , "Beat strongly" , "One's heart may do it" .)