Can I deduct my trip to Isreal as an employee business expense to obtain
My H1B Work Visa renewal? This would include airfare, car rental and
Hotel. My employer will not reimburse me.

Thank you

No, you cannot, because:

1) It is considered to be a personal expense by the IRS.

2) You did NOT have to go to Israel to get the H-1B visa; you could had it done in either Canada or Mexico for a LOT less cost.