We have no khalifah, do we have to strive for it? Please elaborate on this issue.

Yes, we have to struggle for establishing khilafah[1] (the single head of Muslim Ummah), but the important question is on how we strive for it.

 The idea of having a khalifah is from Islam, we cannot say that it’s a Maudoodi idea. Both Hasan al Banna[2] and Maudoodi[3] struggled for establishing Islamic law; they did promote this struggle, the idea that Islamic law should govern Muslims.

The question is on how one goes about establishing the khilafah. The starting point is the correct belief of Muslims (‘aqeedah). We must have correct foundation first and then build the structure over it. The idea that we first make the structure and then later on build a foundation doesn't work. The correct approach is that we must start with our ‘aqeedah, which we have to correct, establish and built on; then we can establish the Islamic State etc. If we don't correct the foundation then whatever we will build will have a weak structure.

Moreover, the minimum that we can all do is to establish Shari’ah in our own lives; that is what Allah is going to ask us about. In whatever walk of life we live, we must strive to establish Shari’ah around that. Allah will question us as to what degree we established Islamic Shari’ah in our own lives, in our family, around our community; He will not ask us as to why we didn’t establish the khilafah. Adhering to Shari’ah in our own live is one of the steps necessary for the establishment of khilafah; our focus should be on what we can actually control. To put our energy and struggle for something that is beyond our control and influence is only wasting our efforts and producing little results.[4]

References:

[1] http://peace-foundation.blogspot.com/2010/11/bilal-philips.html

[2] Sheikh Hasan Ahmed Abdel Rahman Muhammed al-Banna known as Hasan al-Banna (14 October 1906 – 12 February 1949) was a schoolteacher and imam, best known for founding the Muslim Brotherhood, one of the largest and most influential 20th century Muslim revivalist organizations.

http://en.wikipedia.org/wiki/Hassan_al-Banna

[3]Abul A’la Maududi (September 25, 1903 – September 22, 1979) was a journalist, theologian, Muslim revivalist leader and political philosopher, and a controversial 20th century Islamist thinker in India, and later Pakistan.^[2] He was also a political figure in Pakistan and was the first recipient of King Faisal International Award for his services 1979. He was also the founder of Jamaat-e-Islami, the Islamic revivalist party

http://en.wikipedia.org/wiki/Abul_A'la_Maududi

[4] Sheikh Uthaymeen, Sharh al-‘Aqeedah al-Safaareeniyyah, p. 688