Coulthirst, 19, played his first Spurs game as a sub in last month's Europa League win over Anzhi Makhachkala.
He is eligible to make his Orient debut in Saturday's FA Cup tie at Yeovil Town.
Tribal Football Staff are dedicated to the football tribes from all over the world. Our team is passionate about delivering football news to our hundreds of thousands of followers in all the corners of the globe. Football is life, It never stops, Neither do we.