One of the requirements of registration as a registered investment adviser is the appointment of a Chief Compliance Officer and the establishment of a formal compliance program. The SEC stated that a firm need not hire a new person to be the CCO. However, there will be a substantial time commitment.
You can spread some of the compliance work to multiple people in the firm, though the CCO will ultimately be responsible for oversight. Another option is to send some of the work outside the firm that would outsource some or most of the compliance functions.
Insider trading monitoring is one of the candidates for outsourcing. There is a lot of data and a lot of paperwork to track. Even for a private equity firm that does not regularly trade in public securities, there is plenty to keep a person occupied during the week. For a private equity firm, some trade tracking software will go a long way to help the CCO (and the employees) deal with the invasive and tedious requirement to track employee trading.
The SEC rules also require an annual review and update of the compliance policies and procedures. This too is a likely area for outsourcing. A third party can provide additional insight to the firm as to what your peer firms are doing and what issues the regulators are focusing on.