Whatever Meril's arc entails, it will likely be closely tied to the arcs of Orodreth and their children.
Season 4 saw the introduction of Meril's character at the Mereth Aderthad as a Sinda that Orodreth was obviously interested in. Their wedding took place at Minas Tirith the beginning of Episode 6, but the focus of that episode was on Edhellos and (fake) Angrod. Meril and Orodreth dwell with Finrod at Minas Tirith after their wedding, although Orodreth delivers news of the Ban to the Feanorians and goes to Angband with Celebrimbor in Episode 8. In Episode 9, Orodreth returns to Minas Tirith from a visit with his parents on Dorthonion. I am currently in the process of revising all the Season 4 scripts, but I think I am going to have Meril and Orodreth both returning from Dorthonion. Meril is a healer during the Dagor Aglareb, and this is a role she could reprise in future conflicts. In Episode 13, Meril and Orodreth attend Galadriel and Celeborn's wedding, and, in the final montage, they and Angrod are with young Finduilas when she meets Treebeard.
I expect we will meet young Gil-galad and see more of Finduilas in Season 5, so Meril will likely be present for that. She and Orodreth will be ruling Minas Tirith while Finrod is in Nargothrond. Since Minas Tirith is going to feature prominently in Season 6, we should probably not forget about it during Season 5. We might show a council being held there or a visit from Finrod or Fingolfin or someone else. Orodreth and Meril might go to visit Orodreth's family in Dorthonion or Meril's family in the Falas. Such decisions, as Nick said, are generally made when planning details of individual episodes.
Minas Tirith will be captured in either Season 5 or 6, so we will show Orodreth, Meril, and Finduilas fleeing with their people to Nargothrond. One question associated with this is what will happen to Gil-galad at this time? In The Silmarillion, Fingon is Gil-galad's father and sends him to the Havens after Fingolfin's death. We could have Orodreth send Gil-galad away after the Dagor Bragollach (and maybe Meril could go with him), or we could have the family stay together until the fall of Nargothrond.
In Season 6, Orodreth will become king of Nargothrond when Finrod leaves with Beren, Celegorm and Curufin will bring Luthien to Nargothrond, and the people of Nargothrond will drive out Celegorm and Curufin when they learn of Finrod's death. Meril can take part in the scenes we use to depict these events, and she will probably stand by Orodreth whatever he does.
Nargothrond will feature again in later seasons, when Gwindor leads his company to participate in the Nirnaeth and in all the events associated with Turin. Meril can speak in support of or against Gwindor when he leaves, have interactions with Turin, and talk to Finduilas about her feelings. Again, the specifics of Meril's actions will largely depend on the details of the individual episodes.
Meril could die in the Fall of Nargothrond, but she does not necessarily have to. She could die before that, or she could escape Nargothrond and die in the Third Kinslaying or the War of Wrath, or she could survive and sail back to Valinor or stick around during the Second Age when her son is High King.
Meril is a character we pretty much invented, so her arc can be whatever we want it to be. However, we should make sure it supports and fits into the stories Tolkien wrote.