The simple way is to change the clock signal from 200Hz to 1kHz, but it depends on what kind of configuration are used. Usually, a signal generator is used to select the repetition rate. So signal generator can be adjusted to 1kHz. A synchronizer (synchronization circuit) is used where this signal generator which selects repetition rate is connected, along with the oscillator signal by a photodiode, so that to synchronize both the signals.
It is not possible to understand your question exactly. You speak about multipass amplifier or regenerative amplifier ? In general, the available repetition rate of Ti: Sapphire amplifier is determined by pump laser (as a rule, 532 nm Nd:YAG). If you want to operate at 1 KHz, then you must get the appropriate pulsed pump laser at first.
Aleksandr A. Tarasov is right, you need to increase the repetition rate of the pump laser.
However, the most serious issue will be the thermal load. If you increase repetition rate and keep pulse energy you will have 5 times the thermal load. So you will start seeing issues with excessive thermal lenses and damaged crystals.
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