Green’s Dictionary of Slang

hitch up v.

[the hitching up of one’s team to a wagon or coach before setting off on a journey]

(US) to start, to set off.

[US]G.F. Ruxton Life in the Far West (1849) 3: Sam had his train along, ready to hitch up for the Mexican country.
[UK]J. Ware Passing Eng. of the Victorian Era.