In the iOS app for Spotify with a free account if you search for a playlist, click on one, then decide to check out what other playlists that user has you can't click on their username to go to their profile. However, you can in the paid version of Spotify. I suggest this be linked the same way as the paid version instead of having to go back and search for that user (which is also difficult).
Along with the user profile link, this suggestion is also for the playlist description, last updated date and duration to show, the same as the paid version. Please see the screenshots below for reference.