Holding uL tokens allows you to claim UP tokens. Claiming UP tokens is how liquidity providers earn their share of the fees generated by their liquidity. Claiming UP will not change your balance of uL tokens. UP tokens are not claimed automatically except when adding more liquidity or sending uL tokens to a different address.
This can either mean redeeming uL tokens to withdraw your liquidity or redeeming UP tokens in exchange for the base tokens in the redemption value. Both of these actions removes the respective token (either uL or UP) from your wallet.