Is there an expression or saying that can be used to describe when person is growing old and he/she becomes less involved with physical issues and devotes more time to spiritual ones, taking care more of his/her soul rather than his/her body or other everyday issues?
I think the closest phrase to what you're trying to express is 'self-actualises'. The process of self actualisation is at the top of Maslow's hierarchy of needs. More information is here:
He's become sage as the years pass
To be sage, suggests a person who is not only wise, but also rather philosophical and tolerant. A person who has reached a certain stability (or maturity) in life, and doesn't feel the need to prove his (or her) worth.
I would readily use this term for also a woman, despite what Oxford Dictionaries seem to suggest
(Especially in ancient history or legend) a profoundly wise man:
the sayings of the numerous venerable sages
- “Sen Tetsu So Dan: the first two characters mean a great thinker, a wise man, a sage in ancient times, while the third means a group, or a collection.”
I would say that's when the person becomes an Elder in the way Native Americans use it:
“It is important to note that the title “Elder” does not necessarily indicate age. In Aboriginal societies, one is designated an Elder after acquiring significant wisdom and experience.”
(Meadow Lake Tribal Council website)
Elders are people who:
have significant wisdom in areas of traditional aboriginal knowledge. are recognized as having that wisdom by their community, their Nation. have the capacity to transmit this knowledge to others.
Within Native culture, the Elder occupies a revered position: he or she is a person gifted with great wisdom, an individual who advises, resolves disputes, and acts as a model of acceptable behaviour within the Native community. Although Elders are very much an element of reservation life, they are developing a role within the culture of urban Natives.
The Indian equivalent might involve a discussion of Dharma, the general rules and principles governing human existence and relationships, with specific reference to the āśramas:
At the individual level, some texts of Hinduism outline four āśramas, or stages of life as individual’s dharma. These are: (1) brahmacārya, the life of preparation as a student, (2) gṛhastha, the life of the householder with family and other social roles, (3) vānprastha or aranyaka, the life of the forest-dweller, transitioning from worldly occupations to reflection and renunciation, and (4) sannyāsa, the life of giving away all property, becoming a recluse and devotion to moksa, spiritual matters. (see: https://en.wikipedia.org/wiki/Dharma, and https://en.wikipedia.org/wiki/Ashrama_%28stage%29).
Returning to the OP's original question, the āśrama which most closely matches the concept of devoting 'more time to spiritual ones (issues), taking care more of his/her soul rather than his/her body or other everyday issues...' is the stage known as vānprastha (see: https://en.wikipedia.org/wiki/Vanaprastha). The literal translation of this is 'Going into the forest', which suggested retiring to a hermitage or wild place, away from human civilization for a period of self-reflection and study.
If the āśramas within an individuals dharma (path) describe the stages of life, the puruṣārthas (strivings) describe what might impel him or her down that path:
The four stages of life complete the four human strivings in life, according to Hinduism. Dharma enables the individual to satisfy the striving for stability and order, a life that is lawful and harmonious, the striving to do the right thing, be good, be virtuous, earn religious merit, be helpful to others, interact successfully with society. The other three strivings are Artha - the striving for means of life such as food, shelter, power, security, material wealth, etc.; Kama - the striving for sex, desire, pleasure, love, emotional fulfillment, etc.; and Moksa - the striving for spiritual meaning, liberation from life-rebirth cycle, self-realization in this life, etc. The four stages are neither independent nor exclusionary in Hindu Dharma. (see: https://en.wikipedia.org/wiki/Dharma, and https://en.wikipedia.org/wiki/Puru%E1%B9%A3%C4%81rtha)
It is interesting to compare the elements of the puruṣārthas (the four human strivings) with Maslow's hierarchy of needs.