I have installed Fire Brigade app on a search peer, but I'm not able to see host or retention data.
Per the extra documentation "Details", yes, you will need the TA. The TA does the data collection; it live on the indexer nodes (any hosts which have data stored locally, and in some cases this may mean your search head, too!). The FB main app lives on the search head, not the "peer" assuming you meant "indexer" when you said "peer".