The base contract
The principal grants the agent authority to perform a defined task: invest funds, manage a takaful pool, execute a transaction. The agent earns a fee for the service, not a share of profit (which would convert it to a Mudarabah).
The agent's fee can be fixed or scaled (per transaction, per assets under management). It cannot vary with profit alone, because that pattern collapses Wakalah into a profit-sharing structure subject to different rules.
Where Wakalah shows up
Takaful: the takaful operator runs the pool as an agent for the participants. The operator earns a fixed Wakalah fee for managing claims and the underlying investments. Surplus goes back to participants, not to the operator.
Asset management: many halal funds use Wakalah at one or more layers of the structure. The investor authorizes the manager to invest within Sharia-screened parameters; the manager earns a management fee.
Brokerage: a brokerage executing trades on behalf of a customer is a Wakalah relationship. Per-trade or per-transaction fees are standard.