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In the past, new types have mainly been introduced to rebalance things that got out of hand. Fairy's strengths and weaknesses come to mind, as well as lifting two of Steel's resistances to weaken Steel/Psychics and the newly introduced Aegislash.
Things we currently need in one or more types are:
Offensive:
Strong against Ghost, Electric
Weak against Rock, Ice, Psychic
Defensive:
Vulnerable to Bug, Psychic, Poison
Resistant to Ice, Ground, Rock, Fighting
Something related to peace, tranquility and meditation might work as a new type.