partisan : n
1. An adherent to a party or faction.
2. A fervent, sometimes militant, supporter or proponent of a party, cause, faction, person, or idea.
3. A guerilla fighter; a member of detached light troops acting behind enemy lines.
4. (now rare) The commander of a body of detached light troops engaged in making forays and harassing an enemy.
advocate : n
1. Someone whose job is to speak for someone's case in a court of law; a counsel. [from 14th c.]
2. Anyone who argues the case of another; an intercessor. [from 14th c.]
3. A person who speaks in support of something. [from 18th c.]
4. A person who supports others to make their voices heard, or ideally for them to speak up for themselves.
adherent : n A person who has membership in some group, association or religion.
From the above an advocate is someone who speaks or argues for a cause that may not be their own while a partisan belongs to the group, faction, party, for which they are arguing.
The phrase partisan advocate could be describing someone who is an advocate who is arguing along party lines or it could be talking about somebody who advocates on behalf of the partisans. Context should tell you which one is applicable in your case.