The phrase "allow him to explore" is correct and usable in written English.
You can use it when giving permission or encouraging someone to investigate or discover something.
Example: "As part of his learning experience, we should allow him to explore different cultures and traditions."
Alternatives: "permit him to investigate" or "let him discover".
It will allow him to explore some of the early relations between Islam and the West.
He sits up, reaches for me and I allow him to explore me in turn.
A series of jobs in this industry - which is largely fast moving and dynamic - will allow him to explore different roles and settings.
Mr. Murdoch is said to have proceeded with the split this summer in part because a separate publishing company would allow him to explore acquisitions without facing fierce resistance from shareholders, according to several people familiar with the company's thinking.
Fenlands, hinterlands, un-fixed landscapes of all kinds both suit his temperament (he's someone who likes to speak to the centre from the side) and allow him to explore the edges of vision, where beauty and significance are easily overlooked.
Bonamassa's solo albums allow him to explore more varied interests, and last year's best-selling Black Rock was an eclectic set mixing acoustic and Greek themes with the rapid-fire solos.
Writing appealed to him because it allowed him to explore food and wine.
His work allows him to explore what we're normally uncomfortable with".
While attending that camp allowed him to explore his options, he still is partial to playing internationally for the United States.
Throughout the 1990s Dafoe continued to appear in roles that allowed him to explore moral ambiguity in characters.
Berlin felt that his ignorance of the laws of music allowed him to explore original musical combinations that wouldn't have occurred to more educated composers.
