If the agent accepts our offer and we request a finance clause aren’t they obliged to include the clause in the sale contract…. the agent is putting us pressure to exchange?

Aleisha. Hi. Thank you for your question. The standard process in NSW (non Auction) would be to have a five day cooling off period unless you sign what is called a 66w Certificate, which waives your rights to cool off. It is often possible to request the cooling off to be extended to 10 days, this then allows time for finance to be formally approved (assuming you are already Conditionally approved) and also time for pest and building etc.
if you exchange under these conditions you will be asked to pay a 0.25% non refundable deposit. This is "at risk" money, should you not proceed for any reason.
The benefit of exchanging in this manner is that it removes the property from the market and prevents you from being Gazumped. Without an exchange of contract, the property can still be viewed and open to offers from others.
I recommend you make an appointment to see a Conveyancer / Solicitor asap to get full advice.
Hope this has been helpful.
Best Regards
Ken Olds
Director
Customers First Mortgages & Insurance
1300 ASK KEN