Broad projection involving Times beginning to recruit influence in Parliament? (7)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

[ LOBE(a broad projection/a rounded part extending from a larger structure) containing ( involving ) BY(denoting multiplication/times, as in “2 by 2 = ..”) ] + 1st letter of ( beginning to ) “ recruit ”. Answer: … or “lobbyist”, one hired to influence lawmakers/Parliament.