Clue: Old man, twice party leader (4)
Answer: PAPA
Explanation: Definition: Old man
I presume this is PA[rty] twice, though it's a bit of a stretch as (singular) "party leader". *A much better explanation from Larry et al: it's PA (old man) twice,
 with definition "party leader", which is P = PAPA in the NATO phonetic alphabet (or possibly Papa Doc Duvalier, though I'm less convinced by that).