Idiom Definition 1:
"to head up"
to depart and move or travel in an uphill direction
to depart and move or travel north (up on a map)
to depart and move or travel in the direction where the address numbers are increasing
Synonyms:
beat it, bolt, decamp, depart, duck, embark, escape, exit, flee, getaway, go, hightail, leave, march, move, part, run, scram, skedaddle, split, start, vamoose, walk