Third Bridge is not in a position to advise you on whether or not your participation in a consultation would be a conflict of interests.
A conflict of interests in business normally refers to a situation where an individual's personal interests conflict with obligations they have to a company.
In legal terms, a conflict of interests is defined to take place when someone has multiple interests which conflict and may affect their objectivity or ability to perform a duty. I.e. A person has a duty to one party which affects his ability to be impartial in executing a duty toward a third party.