Captain reported during climb they received an ECAM ELEC: DC ESS BUS SHED warning. Flight crew elected to divert and make a precautionary landing.

Narrative

After take off Runway XXL : During Climb at approximately 6;000 ft. we received the ECAM ELEC: DC ESS BUS SHED. As I was Pilot Monitoring; I asked FO (First Officer) to take the radios and continue our departure while I worked the QRC for immediate action or ECAM exceptions. We leveled at 8;000 ft. and discussed the ECAM and I proceeded to accomplish ECAM actions. We then asked ATC for vectors to work on a Maintenance issue. ATC complied and we proceeded with the [company procedure]. After the ECAM was complete I did the ECAM QRH follow up and ECAM Supplemental Manual. As there was no [solution] to the DC ESSENTIAL BUS FAULT; we then [requested priority handling] due ELEC. FO continued to fly and talk with ATC and I tried to contact Dispatch. I could not Find/Use the Crew phone app and later Dispatch provided VHF frequency for voice comm. As we were limited to NO ICING CONDITIONS; I requested Divert to ZZZ which would allow us to burn down fuel to allow normal landing/Not overweight.After we completed the ECAM procedure and follow up; we discussed our options to continue based on the electrical fault and restriction of: AVOID ICING CONDITIONS. I spent several minutes looking in the QRH for the Dispatch Frequencies and the AIRINC Sector Map with ZZZ1 Freq to contact Dispatch through Phone patch. We both discussed continuing to ZZZ2 or ZZZ and elected ZZZ as the more reasonable option for diversion. We wasted time trying to communicate to Dispatch and get Maintenance on line with a phone patch that failed. As I was trying to SOLVE and reset the DC ESS SHED BUS Fault it became apparent that there was no fix while airborne. Subsequent Diversion to ZZZ.The Event was NOT to be avoided and there was no FAULT before take off. Both myself and FO worked as we are trained to do. We employed the [company procedure]. We both communicated well and talked over our options. The issues we had were in establishing Voice communications with Dispatch and Maintenance Control in ZZZ2. In the end we were successful in contact through VHF to Dispatch. The phone patch to Maintenance failed; so I requested Diversion to ZZZ for Maintenance as we knew we could not avoid icing conditions at destination. I suggest adding the ZZZ AIRINC Map with the appropriate Sector Frequencies along with Dispatch VHF Frequencies to the QRH.