I'm not sure if you need it for bacteria or mammalian cells, but you can try CRISPRi? You can target any promoter sequence (endogenous or synthetic) for strong repression when you induce Cas9 expression.
Link to paper: https://www.nature.com/articles/nprot.2013.132
Here's a big review of synthetic biology circuitry in general: https://www.nature.com/articles/s41580-018-0024-z
Mammalian. CRISPRi is an option, but I'd prefer not to have to deliver gRNAs. I was thinking a TALEN fused to a transcriptional repressor like KRAB, but I don't know of any well validated promoter/TALEN combos that would work. It would have to be a synthetic promoter or from a species other than mouse in order to avoid repressing any endogenous genes.
You can use tetO-tTA system (or rtTA). In a nutshell, you have a loci under control of tetO operator. Then you overexpress a tTA (or rtTA) element coupled to some sort of promoter (usually some cell type specific one, or ubiuquitisely expressed one). If you use tTA, upon giving Doxycycline to mice (for example) via drinking water, the tTA will bind to the tetO operator and halt the transcription. Alternatively, if you use rtTA, binding of it to the tetO in presence of Doxycycline will activate the transcription.