The 16-year-old midfielder was on the bench for Saturday's 2-1 defeat to Arsenal, but was not given the opportunity to get on the pitch.
However, with the Baggies in no relegation danger, Clarke has admitted that he may look to keep things fresh over the remaining six matches of the campaign.
"I think in the way that the game evolved on Saturday it wasn't the type of match to bring him in. Don't forget he's not even 16 and a half yet. But it's good to keep him involved. He trained last week and he was excellent and deserved his spot on the bench," he is quoted as saying by the Express & Star.
"It's a great experience for him and, being 16, he'll enjoy days like that. I have told the players before now that I will have a little look at one or two different things. I don't want to become predictable and samey.
"There will be a chance for other players between now and the end of the season. But I think we just need to keep our eye on the ball and know what we are trying to achieve."
Brown is currently taking his GCSEs.