The narrative is a trendy way in current affairs (the news, etc.) to refer to people's opinions about any subject. The term is literary, originally. It is the mechanisms used to tell a story. In literary terms, there are all sorts of narratives.
The point of view people express about various subjects is called "the narrative". At some point, in the last 20 years or so, it became trendy to use this literary term. I cannot locate precisely when that happened. Use of the term narrative also arose in reference to how the press tells the story about some event or other.
For example, if you are referring to some past event (in the news, social history etc.), they can be said to have a narrative (story, basically). When JFK was assassinated, various narratives (ways of explaining it) arose about that event.
But it can also refer to historical oppression where people were not allowed to tell their story or what they experienced. When the sexual abuse scandals of the Catholic Church starting coming out, the church tried to "control the narrative" (what was being said). Then, all these groups and movements arose with real people telling their stories and recounting their experiences. The church was "claiming" this or that. Now, the victims of institutionalized sexual abuse are "reclaiming the narrative". The idea here is that they are saying: These are our stories and we will tell them in our own voices and however we please.
So, the church can be said to be "losing control of the narrative" and those people who are telling their stories are "reclaiming the narrative"; they are taking back what they see as a right to tell their own story without any help from the institution of the church.
So, "reclaim a narrative" means to (re)take control of how a story is told about you or a group you are part of and not let some "authority" be the one who controls it.