WordNet sense 1 (an instinctive motive):

impulse

WordNet sense 2 (a strong restless desire):

itch

WordNet sense 3 (push for something):

advocate, recommend, advocate

WordNet sense 4 (urge on or encourage especially by shouts):

barrack, cheer, exhort, inspire, pep up, urge on

WordNet sense 5 (force or impel in an indicated direction):

press