try this

Well I went to Amazon to get a link for the one I bought, but it looks like it isn't available anymore. I'll go ahead and link it anyway in case it helps. This one works with my Nexus 7 2013 LTE:

https://www.amazon.com/gp/product/B00HFYLR4M

Some things to note:

• The Nexus 7 dispay is 16:10, so 16:9 content gets black bars added to the top and bottom. The HDMI out is 16:9, so black bars are added to the left and right. The end result is that if you watch a 16:9 video on the Nexus using HDMI out, you will have black bars on all 4 sides on the TV. I've seen people saying you can fix this by rooting the device and then typing in a command that changes the internal display to 16:9, but never tried that.
• The cable I linked has a microUSB power input and that does provide power to charge the Nexus. However, the Nexus 7 2013 is not capable of charging as fast power is used when the screen is on and it is playing a video. So, having the power connected there reduces how fast the battery discharges, but it does still slowly drain the battery when playing videos out HDMI.

The main reason I bought this was back when T-Mobile was limited data, but unlimited streaming video, I wanted a solution that allowed me to stream Netflix to hotel TVs without counting against my 2 GB of data.

This is the one I used to use with my Nexus 7:

https://www.amazon.com/gp/product/B00HFYLR4M

It supports charging at the same time. However, the Nexus 7 tends to have very slow charging, and with the screen on displaying a video you're probably going to see it discharging faster than it can charge.

Also, the aspect ratio of the Nexus 7 is 16:10. When you display 16:9 video on the Nexus, it adds black bars on the left and right. When you output the Nexus's 16:10 display onto a 16:9 TV, you add black bars to the top and bottom. The end result is that your video will have black bars around all 4 sides. I never tried it, but I remember reading that you had to root the device to get access to the commands that could change the Nexus' own display to 16:9 to fix this problem.