歩き続けて

keep walking

→ 歩く
歩き walk + 続け continue, keep doing + Te-form (conjunctive)
verb Rare #37,769
keep walking
JA: 歩き続けて、やっと駅に着いた。
EN: I kept walking and finally reached the station.
Conjugation of 歩く
Present
Potential past
Conditional
Potential present
Desiderative
Indicative
Indicative present

ただ歩き続けて

Just keep walking.

何時間も歩き続けてきたのだ

I've been walking for hours.

歩き続けて

Keep walking.

足を出して歩き続けて

Keep putting one foot in front of the other and walk on.

— ハウルの動く城 (2004)