1) In mining contexts this was a passage ‘driven’ or excavated.
1717 Agreed then with Adam Harrison to drive me a drift at Farnley Moore at Low end of the down end in the pitt we are now working, Farnley
1754 for ale for the men that sate up in the night in the drift, Beeston
1761-3 on Acct of driving Drift at Combs Colliery in part of Ł39, Lepton. The word occurs earlier in lead-mining documents: 1682 he might carry on the works on driving drifts and sinking shafts, Healaugh.
2) The driving of cattle or horses, moving them together in herds or flocks.
c.1570 the dryft of the cattell dyd disturbe the bredyng of the wyld fowle, Leconfield
1599 also one sufficient waye ... for drifte of Cattell in over and through the Northe Ende of one parcell of land, North Bierley.