The Baggies boss has been hugely impressed with the talent he's found being nurtured in the academy and has already given minutes on the pitch this season to Sam Field, 18, Jonathan Leko, 17, and Kane Wilson, 16.
He named Field, Wilson and 16-year-old Harper on the bench for Saturday's FA Cup tie with Derby County.
Although none of them were used, Pulis is eager for all three to taste men's football this season and hopes to send them out on loan.
Harper is just the latest teenager to catch the eye in training.
He first travelled to an away game with the squad in November when the Baggies beat Leicester City at the King Power Stadium, and then he was named on the bench for December's home win over Swansea.
A former striker, he has been converted to a dynamic box-to-box midfielder versatile enough to play a holding role or behind the striker if required.
Pulis believes Harper has the skill-set necessary to succeed, but now he's challenged the young midfielder to show some grit and determination to match it.
"Rek has done fantastic," said Pulis. "He's a young midfield player who is only 16, but he's got all the tools to be a player. He's another one who's got to take his gloves off and get his hands dirty. Find out what it's all about.
"As I keep saying, academy football is not just about developing your skills, it's about learning your trade.
"You don't learn your trade by having your gloves on all the time and not going out and getting cold."
Pulis reckons the best way to do that is to go out on loan to lower league clubs and taste men's football in a pressurised environment.
He's hoping the club will do enough business in January to allow him to send the youngsters out on loan.
"If we can bring players in then maybe (we can loan them out)," he said. "At the moment those players are training with us.
"We had three youngsters on the bench on Saturday. If we can get the group that we want, it gives us the option for us to get them out.
"I am really keen to get those kids playing; Sam, Kane and Rekeem."
Albion have recalled forwards Tyler Roberts, 17, from Oxford United; Tahvon Campbell, 19, from Yeovil Town and Andre Wright, 20, from Coventry, and now plan to find them new clubs.
Defender Kyle Howkins, 20, has remained at League Two Mansfield Town and played 90 minutes in their 3-0 win over Crewe on Saturday.
Shaun Donnellan, 19, came off the bench for National League side Dagenham & Redbridge in the 89th minute.