Hi, you should put the diode (remember it still will be cliping indicator just for one side, if you have assymetrical signal may clip and not light if you use it as clipping detector, for signal presence would be OK unless you have a big negative DC Offset when led will be always on)
If you just want it to work only put the diode in its place and should be working and stop reading, if you want to go deeper on the circuit keep reading.
Remember INA163 is a complete mic pre, I assume you change the mic input for a line one.
Without the diode 10k 1µ will act as low pass filter at 15Hz so no audio signal will reach neither the 2nd opamp nor the LED. With the diode this will act as 10ms attack, so not realy a peak detector (5ms standard)
If you want an standard peak detector use 5K for R1 and 650K for R2. If you want clip detector at 600Ω using LM833 put 4K7 for R4 and 10K for R3 (about 19 dBu) 7K5 (2 15K in parallel) seems a little low for driving the led, but if the bright is OK they are working fine, if they turn on but not so bright as you want you could lower this value. Just a recomendation, don't use the same IC for both opamps, you could hear a click when the diode turns on and off because crosstalk and the current draw of the led, for even less noise you should use another ground path and decoupling caps for the supply rails.
Cheers.
JS