In early life, Scrope served in the Scottish campaign of 1333 and was knighted at Berwick, where he fought at the Battle of Halidon Hill.
He served in Scotland again in 1335 and in 1340 took part in the sea Battle of Sluys at the start of the Hundred Years War.
In 1359 he served under John of Gaunt in the great chevauchée toward Rheims, and in 1361 he was appointed Warden of Calais and Guînes until 1370.
In 1369 he served under John of Gaunt in France; and in 1371 was for a year warden of the western march towards Scotland and also steward of the king's household.
Scrope had married twice; firstly to Agnes and secondly to Joan (both surnames are uncertain).