The star increases exist, but most traits are mission specific so won't increase the overall number of stars displayed. However, after 4 successful killings, yours should have at least +2 on assassination missions so 5 stars total in that case. Other traits boost sabotage, hiding&spotting, duel with swords or pistols etc...
I don't think I've seen a trait line that'd boost general purpose stars besides the ones they sometimes spawn with.
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