To daresay is to suppose that something is probably so. I daresay you are right, I daresay it will rain, daresay so.
It only really occurs in the first person present — I daresay — where it works as a hedge meaning I expect, often with a shade of politely declining to argue. It is British and slightly old-fashioned. Note that it is written as one word or two, and that dare in it keeps its old sense of venturing rather than defying.
1verbdaresayTo suppose that something is probably so.
“I daresay you'll feel better after a good night's sleep.”
daresay is a supposing.
A running together of dare and say. The old sense of dare, to venture, is what survives in it.
From dare say: dare + say.
Etymology from Wiktionary, CC BY-SA
Practised in A Song of Ice and Fire