Don't increase it!
From Fallen London Wiki
For an early player by <a href="/wiki/Meet_some_Constables_you_know" title="Meet some Constables you know">Meet some Constables you know</a> in <a href="/wiki/Mrs_Plenty%27s_Carnival" title="Mrs Plenty's Carnival">Mrs Plenty's Carnival</a>. <a href="/wiki/Tea_with_the_Inspector" title="Tea with the Inspector">Tea with the Inspector</a> will unlock if Renown: Constables reaches level 5. It only pollutes your fortune desk.
