Some say Shiva is the supreme God.
Some say Shiva is energy and cannot be destroyed.
I agree on both !!!
But does this mean Lord Shiva will reincarnate himself with the birth of Prithvi ?
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Destruction and Creation of Prithivi is Kalpantaka pralaya. Ie. Destruction and creation of Prithivi ( also Swarga and Patala) takes place in each day of Brahma.
It doesn't affect to Lord Rudra at all. Actually it is Lord Rudra himself who runs Pralaya. Also Parvati / wife of Lord Rudra isn't affected by simple things like this Kalpantaka Pralaya. Actually as discussed in this answer present Parvati has life span of Six months of Brahma:
In this Varaha Kalpa, O goddess, you became Parvati obtained by Himavan through his penance, when the Chakshusha Manvantara has passed off. O beautiful lady, due to the anger of Daksha you had to be separated from me for the duration of a day of Brahma. Your span of life is the period of his six months.
ie. Present Parvati lives for about 6 × 30 = 180 kalpas. Then something may happen and she may leave her body. So the destruction and creation of Prithivi doesn't affect to Rudra/Parvati at all. ie. It is not necessary to reincarnate at all.
However after the Mahakalpa (when Brahmas 100 years is over) then Lord Rudra also may merge back to Lord Shiva as I discuss in my answer here:
अन्ये च ये समुत्पन्ना यथानुक्रमतो लयम् ।
यान्ति नैव तथा रुद्रः शिवे रुद्र विलियते ।।
Others which have origin finally dissolve as per their process. However Rudra merges back to Shiva himself.
Now, when New Brahma comes Lord Shiva again incarnates as Mahadeva as described in this chapter of Atharvaveda. He also takes AshtaMurti forms as described in this chapter of YajurVeda Satapatha Brahmana. Similarly he also does all works assigned to him by Vedas as stories described in Vedas are eternal. Some of the works I discuss in my answer here. In this way the cycle continues. Shakti of Shiva which is Prakirti herself again incarnates in Human form to meet with Lord Rudra which is given by Lord Rudra to Lord Brahma to assist the creation. And also the cycle of Sati-Parvati goes on which represents meeting of Prakirti and Purusha again and again.