。
The gatekeeper let me pass through the gate.
Literal
Gatekeeper [topic-は] gate [obj-を] pass-through [nom-の][obj-を] permit-[favor-てくれた].
The nominalizer の turns 通り抜ける ('pass through') into a direct object of 許す ('permit'). ~てくれた marks the gatekeeper's permission as a favor to the speaker. 通り抜ける is a compound verb: 通る ('pass') + 抜ける ('come out through').