What will the pilot do if all the airspeed indicators fail?
Some aircraft have angle of attack indicator, but most don't even though they have the sensor and use it for stall warning.

What you normally have is an unreliable airspeed procedure. This generally says that you should, depending on phase of flight, maintain specific pitch, set specified thrust and then adjust for rate of climb/descent while keeping the pitch.

Since aircraft is trimmed for speed, generally the procedure calls for being light on controls and correct mainly with engines. Exception is Airbus which keeps auto-trimming even with speed disagree warning on, so there side-stick controls climb and power controls pitch almost independently.

See also unreliable airspeed procedure for A330.