Add a background counter that tallies wins with a particular character and reward that character with a shard every X wins.
This mechanic is similar to what is seen Pokemon Go where the more you use a character, the stronger they get. Players have favorite characters. Having those characters improve feels good. Each cover and shard earned/won (regardless of amount) gives the player a sense of accomplishment.
The counter for this can remain in the background with no changes to the UI. The counter would track wins with that character only and provide the character with 1 shard every 5 wins, for example. This is an extension of the Favorite mechanic currently applied in-game.
Currently, players favorite a character as a means to obtain shards for the character they ultimately want. This is a passive use of a character since the character is not actually utilized. Adding this experience reward mechanic would encourage players to actually use the favorited character. For example, I may favorite 3* Hawkeye, but use 3* Wolverine as my third in Deadpool Daily. This reward opportunity would encourage me to not only favorite my 3* Hawkeye, but use him on a team in Deadpool Daily.