Earlswood is on a summer break following his decent effort when fourth to Hurricane Lane in the Irish Derby.
The son of Pivotal had a troubled passage in the colts’ Classic at the Curragh yet belied his odds of 28-1 with a big run.
He had earned his place in that exalted line-up by winning the Group Three Gallinule Stakes at the same track in May.
“He’s good and has gone on a little break,” said Murtagh.
“I’m not sure where we’ll go with him. We’re going to speak to the owner and get a plan for the autumn.”
Earlswood holds an entry in the Comer Group International Irish St Leger back at the Curragh in September.
Murtagh is also allowing sprinter Urban Beat a holiday after ending a busy spell with a creditable third to Winter Power in the City Walls Stakes at York on Saturday.
“He ran well. The filly that won (Winter Power) looked good,” said the County Kildare handler.
“We’re going to give him a break now. He’s been busy so we’re going to give him a break and freshen him up and get him back in the autumn.”
Murtagh revealed Fourhometwo has left his yard to continue his career in Australia.
The Ajaya gelding ended his spell with Murtagh on a high by winning the Listed Celebration Stakes at the Curragh.
“The owners have taken him to Australia and he’s going to continue his career out there,” he said.