There are different ways to train your apprentice hunting and battle training based on which apprentice you get.
Juniperpaw: Gorsefur (hunting), Hawkfeather (battle training)
Cloverpaw: Willowclaw (hunting), Hawkfeather (battle training)
Blizzardpaw: Gorsefur (hunting), Hawkfeather (battle training)
Starlingpaw: Gorsefur (hunting), Willowclaw (battle training)
The way you train time spent outside camp is by going outside FireClan territory. Personally, I use this time to talk to other characters in the other clans.