Celebrian is not much of a solider in the same way that Tauriel or Eowyn is. Having the parents that she has, she was given an extensive education which included being taught how to use weapons, but she never excelled in it. She was skilled enough to be able to defend herself, but never really enjoyed it.
Where she thrived was in councils. It wasn’t until Celeborn, Galadriel and Celebrian came to Lothlorien that she was permitted to be a senior member of councils (dealing with both domestic and forgein affairs), but always took an interest in history, economics and politics. In any meeting or council, if she felt someone was wrong she would not hesitate in telling them why they were wrong, and offer alternatives (although this is not to say she did not know when to hold her tongue, which she most certainly did). She had the ability to floor anyone who tried to discredit her or her ideas, and had a good handle on the high politics of Middle Earth.
When she became the Lady of Imladris she was involved in trade and relations between other realms as much as Elrond, and often acted as a diplomat, taking on the roles of the Ladyof the House, as a senior councilor, and as a senior advisor.